Embedded Quantum Cluster Research Articles

DFT study of nitrided zeolites: Mechanism of nitrogen substitution in HY and silicalite

We have performed embedded-cluster calculations using density functional theory to investigate mechanisms of nitrogen substitution (nitridation) in HY and silicalite zeolites. We consider nitridation as replacing Si–O–Si and Si–OH–Al linkages with Si–NH–Si and Si–NH 2–Al, respectively. We predict that nitridation is much less endothermic in HY (29 kJ/mol) than in silicalite (132 kJ/mol), indicating the possibility of higher nitridation yields in HY. To reveal mechanistic details, we have combined for the first time the nudged elastic band method of finding elusive transition states, with the ONIOM method of treating embedded quantum clusters. We predict that nitridation of silicalite proceeds via a planar intermediate involving a ▪ ring with pentavalent Si, whereas nitridation of HY is found to proceed via an intermediate similar to physisorbed ammonia. B3LYP/6-311G(d,p) calculations give an overall barrier for silicalite nitridation of 343 kJ/mol, while that in HY is 359 kJ/mol. Although the overall nitridation barriers are relatively high, requiring high temperatures for substitution, the overall barriers for the reverse processes are also high. As such, we predict that once these catalysts are made, they remain relatively stable.

Quantum Monte Carlo study of strongly correlated electrons: Cellular dynamical mean-field theory

We study the Hubbard model using the Cellular Dynamical Mean-Field Theory (CDMFT) with quantum Monte Carlo (QMC) simulations. We present the algorithmic details of CDMFT with the Hirsch-Fye QMC method for the solution of the self-consistently embedded quantum cluster problem. We use the one- and two-dimensional half-filled Hubbard model to gauge the performance of CDMFT+QMC particularly for small clusters by comparing with the exact results and also with other quantum cluster methods. We calculate single-particle Green's functions and self-energies on small clusters to study their size dependence in one- and two-dimensions.

Modeling Proton Transfer in Zeolites: Convergence Behavior of Embedded and Constrained Cluster Calculations

We have studied the convergence properties of embedded and constrained cluster models of proton transfer in zeolites. We applied density functional theory to describe clusters and ONIOM to perform the embedding. We focused on converging the reaction energy and barrier of the O(1) to O(4) jump in H-Y zeolite as well as vibrational and structural aspects of this jump. We found that using successively larger clusters in vacuo gives convergence of this reaction energy to 14 ± 2 kJ mol(-)(1) and the barrier to 135 ± 5 kJ mol(-)(1) at a cluster size of 5 Å, which contains 11 tetrahedral (Si or Al) atoms. We embedded quantum clusters of various sizes in larger clusters with total radii in the range 7-20 Å, using the universal force field as the lower level of theory in ONIOM. We found convergence to the same values as the constrained clusters, without the use of reactive force fields or periodic boundary conditions in the embedding procedure. For the reaction energy, embedded cluster calculations required smaller clusters than in vacuo calculations, reaching converged reaction energies for quantum systems containing at least 8 tetrahedral atoms. In addition, optimizations on embedded clusters required many fewer cycles, and hence much less CPU time, than did optimizations on comparable constrained clusters.

Theoretical study of the group-IV antisite acceptor defects in CdGeAs2

Native and impurity antisite point defects in CdGeAs2 are studied here using an embedded quantum cluster model based on density functional theory. The calculated geometric relaxations and spin densities of the antisite defects considered here show a clear and distinct difference in the nature of native (i.e. [GeAs]) and impurity (i.e. [CAs] and [SiAs]) antisite defects in CdGeAs2. For the native antisite acceptor, the hole appears to be delocalized in contrast to impurity antisites where the hole is mainly localized at the acceptor site.

Effect of dielectric polarization on the properties of charged point defects in insulatingcrystals: the nitrogen vacancy in AlN

Large unit cell calculations of the properties of charged point defects in insulators largelyneglect dielectric polarization of the crystal, because the periodically repeatedcells are so small. Embedded quantum cluster calculations with shell-modelcrystals, representing a single defect in a large crystal, are able to representthe polarization more realistically. For such embedded quantum clusters, weevaluate the optical excitation energy for the nitrogen vacancy in charge state(+3):vN3+ in AlN. This is done with and without dielectric polarization of the embedding crystal. Adiscrepancy of a few per cent is found, when both ground and excited state orbitals arewell-localized within the vacancy. We show that the discrepancy rises rapidly as the excitedstate becomes more diffuse. We conclude that an embedded cluster approach will berequired for transitions that involve even somewhat diffuse states. The investigation isbased on a new model for AlN that shows promise for quantitative accuracy.

F center inBaF2:Diffuse excited state

The optical properties of the F center in ${\mathrm{BaF}}_{2}$ are of importance because the F center is a product of radiation damage when the material is used as a luminescent radiation detector. Its optical excitation energy is 2.03 eV, experimentally. We have applied computational modeling to study this process. Our method is based on a quantum molecular cluster containing the defect, embedded in a shell-model crystal. When the excess electron of the F center is kept localized in the molecular cluster, an excitation energy of 3.33 eV is found. When the F-center electron is allowed to become much more diffuse, the ground state remains within the vacancy, but the excited state delocalizes, and the excitation energy drops to about 2.56 eV, but the model is inaccurate because quantum-mechanical features of distant ions are omitted. A polaronic representation of the single diffuse electron is then carefully incorporated with the embedded quantum cluster treatment of the system. The polaron in ${\mathrm{BaF}}_{2}$ is found to be beyond the intermediate-coupling regime. Feynman's path-integral results for Fr\ohlich's polaron model give an effective mass of 3.12, in units of band mass. The resultant estimate of F-center excitation energy is 2.04 eV. The successful combination of a quantum molecular cluster modeling element with bulk crystal modeling elements (band mass and polaron correction) warrants further study along these lines. Quantitative and physical limitations of the method and results are discussed.

Electronic structure of crystals: Embedded quantum cluster with overlap

AbstractWe consider a crystal as partitioned into a localized molecular cluster (containing a defect or not) and an embedding region. Within the Hartree–Fock formalism, an expression is derived for an effective potential due to the embedding region of crystal. This potential is part of the cluster Fock operator and requires input from a perfect crystal calculation. Special features of the derivative are rigorous inclusion of cluster‐embedding overlap and orthogonality between single‐electron states of the embedding region and the function‐space manifold of the cluster; physically correct normalization of the Fock eigenstates; and a nontrivial total‐energy algorithm. Computational requirements are qualitatively compared with those for an isolated cluster. The method allows for intracluster (and intraembedding) correlation and can be adapted straightforwardly to local density functional approaches. Fundamental aspects of the embedding problem are addressed in a general formulation that is, nevertheless, oriented toward explicit calculations. © 1995 John Wiley & Sons, Inc.

Crystal excitation: survey of many-electron Hartree-Fock calculations of self-trapped excitons in insulating crystals

To model successfully the diversity of electronic structure exhibited by excitons in alkali halides and in oxide materials, it is necessary to use a variety or combination of theoretical methods. In this review we restrict our discussion to the results of embedded quantum cluster calculations. By considering the results of such studies, it is possible to recognize the general similarities and differences in detail between the various exciton models in these materials.

Calculation of properties of charged defects in BaFBr and SrFCl.

Embedded quantum clusters treated by Hartree-Fock methods have been used to model ${\mathit{V}}_{\mathit{K}}$ (molecular halogen anion) and impurity (${\mathrm{O}}^{2\mathrm{\ensuremath{-}}}$, ${\mathrm{O}}^{\mathrm{\ensuremath{-}}}$, and ${\mathrm{OH}}^{\mathrm{\ensuremath{-}}}$) centers within SrFCl and BaFBr. Different representations involving either fixed-point ions or shell-model ions have been considered as the embedding ions. The results consistently show that the out-of-plane ${\mathrm{Cl}}_{2}^{\mathrm{\ensuremath{-}}}$ or ${\mathrm{Br}}_{2}^{\mathrm{\ensuremath{-}}}$ ${\mathit{V}}_{\mathit{K}}$ center is the most easily formed of the possible ${\mathit{V}}_{\mathit{K}}$ centers. Oxygen ions (${\mathrm{O}}^{2\mathrm{\ensuremath{-}}}$) substituted at a halide ion site attract a neighboring halide ion vacancy and form an energetically stable trap for holes. It is found that upon ionization the resulting ${\mathrm{O}}^{\mathrm{\ensuremath{-}}}$ species is displaced along the c axis when substituted for ${\mathrm{Cl}}^{\mathrm{\ensuremath{-}}}$ or ${\mathrm{Br}}^{\mathrm{\ensuremath{-}}}$, but remains on site when substituted for ${\mathrm{F}}^{\mathrm{\ensuremath{-}}}$. The different levels of calculation show qualitative similarities in ionization potential and charge distribution of the defects.

Theoretical simulation of VK-centre migration in KCl. I. A quantum-chemical study

Using embedded quantum cluster models, the authors have studied the mechanism of VK-centre 60 degrees reorientation in KCl and LiCl, and have considered the possibility that both one-centre 'dielectric' polarons and 'molecular' polarons (VK centres) coexist in KCl. These studies have shown that lattice polarization lowers the activation energy for VK reorientation since the VK centre strongly polarizes near the barrier point. The calculated adiabatic barrier for VK reorientation is 0.63 eV, in reasonable agreement with the available experimental data. From the self-trapping energy calculations and the analysis of the structure and mechanism of the diffusion of the one-centre 'dielectric' polaron, it is apparent that it transforms adiabatically into a VK centre without an energy barrier.

Modeling Localized Defects in Ionic Materials Using Mott‐Littleton and Embedded Quantum Cluster Methodology

Embedded quantum cluster and Mott‐Littleton techniques are used to study defects in MgO, UO2, and FeO. Through these calculations we illustrate the importance of lattice relaxation and provide evidence that the quantum cluster methodology is both compatible with and complementary to a Born‐like ionic model. We discuss the limitations of both methods. Within the Mott‐Littleton framework we consider the derivation of effective pair potentials, region sizes, and the application to complex systems. For embedded quantum cluster calculations we investigate basis sets and discuss effective embedding procedures.

The behaviour of helium in UO2: Solution and migration energies

Detailed simulation study of the properties of helium in uranium dioxide using classical Mott-Littleton and embedded quantum cluster methodologies

Impurity potentials derived from embedded quantum clusters: Ag+ and Cu+ transport in alkali halides

Short-range shell-model potentials between substitutional Ag+ ions and host-lattice halide ions in RbCl, KCl, NaCl, and NaF are derived using the ICECAP methodology. In this method the impurity and its nearest neighbours are treated as an embedded quantum cluster in unrestricted Hartree-Fock self-consistent field approximation. The embedding lattice is described by the shell model. The consistency of the derivation is tested in various ways. The potentials are then applied to calculate activation energies for diffusion by vacancy and interstitial mechanisms for Ag+. Previously derived potentials for Cu+ are used to calculate interstitial diffusion activation energies in KCl and NaCl. The potentials are tested for transferability from one host crystal to another. Deficiencies of the method are discussed and improvements are identified.